3.1 Exact numbers

Some numbers are represented as exact numbers: there is no loss of information when such a number is converted from its mathematical value to its internal representation. On exact numbers, the elementary operations (+, -, *, /, comparisons, …) compute the completely correct result.

In CLN, the exact numbers are:

• rational numbers (including integers),
• complex numbers whose real and imaginary parts are both rational numbers.

Rational numbers are always normalized to the form numerator/denominator where the numerator and denominator are coprime integers and the denominator is positive. If the resulting denominator is 1, the rational number is converted to an integer.

Small integers (typically in the range -2^29…2^29-1, for 32-bit machines) are especially efficient, because they consume no heap allocation. Otherwise the distinction between these immediate integers (called “fixnums”) and heap allocated integers (called “bignums”) is completely transparent.

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